To determine the expression for the area of a square where each side length is [tex]\((x-5)\)[/tex] units, we can follow these steps:
1. Understand the problem: We are given that each side of the square is [tex]\((x-5)\)[/tex] units.
2. Area of a square: The area [tex]\(A\)[/tex] of a square is found by squaring the length of one of its sides. If [tex]\(s\)[/tex] is the side length, then the area [tex]\(A\)[/tex] is given by [tex]\(A = s^2\)[/tex].
3. Substitute the given side length: Here, the side length [tex]\(s\)[/tex] is [tex]\((x-5)\)[/tex]. Substituting [tex]\(x - 5\)[/tex] for [tex]\(s\)[/tex], we get:
[tex]\[
A = (x - 5)^2
\][/tex]
4. Expand the squared binomial: We need to expand the expression [tex]\((x - 5)^2\)[/tex]. Using the binomial expansion formula [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex], we can expand [tex]\((x - 5)^2\)[/tex] as follows:
[tex]\[
(x - 5)^2 = x^2 - 2 \cdot x \cdot 5 + 5^2
\][/tex]
5. Simplify the expression: Calculate each term in the expansion:
[tex]\[
x^2 - 2 \cdot x \cdot 5 + 25 = x^2 - 10x + 25
\][/tex]
6. Look for the matching answer choice: The simplified expression for the area is [tex]\(x^2 - 10x + 25\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{x^2 - 10x + 25}
\][/tex]
